Q. What is the integral of tan(x) dx? (2023)
A.
-ln
B.
cos(x)
C.
+ C
D.
ln
.
sin(x)
.
+ C
.
ln
.
tan(x)
.
+ C
.
-ln
.
sin(x)
.
+ C
Show solution
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer:
A
— -ln
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Q. What is the integral of tan(x) with respect to x? (2021)
A.
-ln
B.
cos(x)
C.
+ C
D.
ln
.
sin(x)
.
+ C
.
ln
.
tan(x)
.
+ C
.
-ln
.
sin(x)
.
+ C
Show solution
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer:
A
— -ln
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Q. What is the integral of tan(x)? (2021)
A.
-ln
B.
cos(x)
C.
+ C
D.
ln
.
sin(x)
.
+ C
.
ln
.
tan(x)
.
+ C
.
-ln
.
sin(x)
.
+ C
Show solution
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer:
A
— -ln
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Q. What is the integral of x^2 with respect to x? (2021)
A.
(1/3)x^3 + C
B.
(1/2)x^2 + C
C.
(1/4)x^4 + C
D.
(1/5)x^5 + C
Show solution
Solution
The integral of x^n is (1/(n+1))x^(n+1) + C. Here, n=2, so the integral is (1/3)x^3 + C.
Correct Answer:
A
— (1/3)x^3 + C
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Q. What is the integral of x^3 + 2x? (2021)
A.
(1/4)x^4 + x^2 + C
B.
(1/3)x^3 + x^2 + C
C.
(1/4)x^4 + (1/2)x^2 + C
D.
(1/5)x^5 + (1/2)x^2 + C
Show solution
Solution
Integrating term by term, ∫x^3dx = (1/4)x^4 and ∫2xdx = x^2. Thus, ∫(x^3 + 2x)dx = (1/4)x^4 + (1/2)x^2 + C.
Correct Answer:
C
— (1/4)x^4 + (1/2)x^2 + C
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Q. What is the integral of x^n where n ≠ -1? (2021)
A.
(1/n)x^(n+1) + C
B.
(1/(n+1))x^n + C
C.
(1/(n+1))x^(n+1) + C
D.
nx^(n-1) + C
Show solution
Solution
The integral of x^n is (1/(n+1))x^(n+1) + C, provided n ≠ -1.
Correct Answer:
C
— (1/(n+1))x^(n+1) + C
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Q. What is the integrating factor for the equation dy/dx + (1/x)y = 2?
A.
x
B.
e^(ln(x))
C.
e^(ln(x^2))
D.
1/x
Show solution
Solution
The integrating factor is e^(∫(1/x)dx) = e^(ln(x)) = x.
Correct Answer:
C
— e^(ln(x^2))
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Q. What is the integrating factor for the equation dy/dx + 2y = 3?
A.
e^(2x)
B.
e^(-2x)
C.
e^(3x)
D.
e^(-3x)
Show solution
Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer:
A
— e^(2x)
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Q. What is the integrating factor for the equation dy/dx + 2y = 6?
A.
e^(2x)
B.
e^(-2x)
C.
e^(6x)
D.
e^(-6x)
Show solution
Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer:
A
— e^(2x)
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Q. What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)
A.
8 cm
B.
12 cm
C.
10 cm
D.
6 cm
Show solution
Solution
Using Pythagoras: (radius)² = (distance from center)² + (half chord)²; 10² = 6² + (half chord)²; half chord = 8 cm, so full chord = 16 cm.
Correct Answer:
A
— 8 cm
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Q. What is the length of a chord that is 6 cm from the center of a circle with a radius of 10 cm? (2019)
A.
8 cm
B.
12 cm
C.
10 cm
D.
6 cm
Show solution
Solution
Using Pythagoras: chord length = 2√(r² - d²) = 2√(10² - 6²) = 2√(100 - 36) = 2√64 = 16 cm.
Correct Answer:
A
— 8 cm
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Q. What is the length of a diameter of a circle with a radius of 7 cm? (2022)
A.
14 cm
B.
21 cm
C.
7 cm
D.
28 cm
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Solution
Diameter = 2 × radius; Diameter = 2 × 7 cm = 14 cm.
Correct Answer:
A
— 14 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
A.
10.47 cm
B.
15.71 cm
C.
20.94 cm
D.
25.13 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer:
A
— 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (Use π = 3.14) (2023)
A.
10.47 cm
B.
15.71 cm
C.
20.94 cm
D.
25.13 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer:
A
— 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021)
A.
10.47 cm
B.
12.57 cm
C.
15.71 cm
D.
20.94 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer:
B
— 12.57 cm
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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
A.
2π cm
B.
4π cm
C.
π cm
D.
8 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. What is the length of an arc of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14) (2020)
A.
6.28 cm
B.
3.14 cm
C.
12.56 cm
D.
9.42 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 6 cm = 6.28 cm.
Correct Answer:
A
— 6.28 cm
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Q. What is the length of an arc of a circle with radius 5 cm and angle 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
6.00 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. What is the length of the diagonal of a cuboid with dimensions 2, 3, and 6? (2022)
A.
√49
B.
√45
C.
√36
D.
√50
Show solution
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.
Correct Answer:
A
— √49
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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)
Show solution
Solution
Diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (4, 0), (4, 3), and (0, 3)? (2021)
Show solution
Solution
Length of diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)
Show solution
Solution
Diagonal length = √[(5-1)² + (4-1)²] = √[16 + 9] = √25 = 5.
Correct Answer:
B
— 5
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Q. What is the maximum area of a triangle with a base of 10 cm and height as a function of x? (2020)
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 10 * x. Max area occurs when x = 10, giving Area = 50.
Correct Answer:
B
— 50
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Q. What is the maximum area of a triangle with a base of 10 cm and height varying with x? (2021)
Show solution
Solution
Area = 1/2 * base * height. Max area occurs when height is maximized, thus Area = 1/2 * 10 * 10 = 50.
Correct Answer:
B
— 50
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Q. What is the maximum area of a triangle with a base of 10 m and height as a function of x? (2021)
A.
25 m²
B.
50 m²
C.
30 m²
D.
20 m²
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 10 * x. Max area occurs at x = 10, giving 50 m².
Correct Answer:
B
— 50 m²
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Q. What is the maximum area of a triangle with a base of 10 units and height as a function of x? (2020)
Show solution
Solution
Area = 1/2 * base * height = 5h. Max area occurs when h = 10, giving area = 50.
Correct Answer:
B
— 50
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Q. What is the maximum area of a triangle with a base of 10 units and height as a function of the base? (2021)
Show solution
Solution
Area = 0.5 * base * height. Max area occurs when height is 10, giving Area = 0.5 * 10 * 10 = 50.
Correct Answer:
B
— 50
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Q. What is the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48? (2023)
Show solution
Solution
The maximum height occurs at t = -b/(2a) = 1. h(1) = 64.
Correct Answer:
B
— 64
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Q. What is the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 48? (2021)
Show solution
Solution
The maximum height occurs at t = -b/(2a) = -64/(2*-16) = 2. h(2) = -16(2^2) + 64(2) + 48 = 80.
Correct Answer:
B
— 64
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Showing 781 to 810 of 973 (33 Pages)
Mathematics (MHT-CET) MCQ & Objective Questions
Mathematics plays a crucial role in the MHT-CET exams, serving as a foundation for various scientific and engineering disciplines. Practicing MCQs and objective questions not only enhances your problem-solving skills but also boosts your confidence in tackling important questions during exams. Engaging with practice questions is essential for effective exam preparation, helping you identify your strengths and areas that need improvement.
What You Will Practise Here
Algebra: Understanding equations, inequalities, and functions.
Geometry: Key concepts of shapes, theorems, and properties.
Trigonometry: Ratios, identities, and applications in problems.
Calculus: Basics of differentiation and integration.
Statistics: Data interpretation, mean, median, and mode.
Probability: Fundamental principles and problem-solving techniques.
Coordinate Geometry: Graphing lines, circles, and conic sections.
Exam Relevance
Mathematics is a significant component of various examinations including CBSE, State Boards, NEET, and JEE. In these exams, you can expect a mix of direct application questions and conceptual problems. Common question patterns include multiple-choice questions that test your understanding of formulas, definitions, and theorems, making it imperative to be well-versed in the subject matter.
Common Mistakes Students Make
Misinterpreting the question, leading to incorrect answers.
Overlooking the importance of units in calculations.
Rushing through problems without checking for calculation errors.
Neglecting to review fundamental concepts before advanced topics.
FAQs
Question: What types of questions can I expect in Mathematics (MHT-CET)?Answer: You can expect a variety of MCQs that cover theoretical concepts, problem-solving, and application-based questions.
Question: How can I improve my performance in Mathematics (MHT-CET)?Answer: Regular practice of Mathematics (MHT-CET) MCQ questions and understanding the underlying concepts will significantly enhance your performance.
Start solving practice MCQs today to test your understanding and sharpen your skills. Remember, consistent practice is the key to success in Mathematics (MHT-CET) and achieving your academic goals!
